# STUDIO DEL COMPORTAMENTO IN REGIME PERMANENTE # Fuzo trfrto quzo ffrzl rror pr gl rvt l rgolzo. So trt quto puto llo tuo ll proprt rg t cotrollo, ch o tto tguro t rvto t rgolzo. Co rfrto tl proprt ott u clfczo qut t otvol tr portz ll procur t. Il coportto rg prt crttrzz co rfrto ll l ll rror ch vrfc rpot gl coc. Co g ccto, gl coc orlt ut oo gl gro, rp lr, rp prolc co v, l cu pro fuzo l tpo l loro L trfort o rchto u tll prcz. Ao ch g tto ch, co rfrto llo ch locch fgur, fclt grlzzl, corro l t cotrollo tr ottopoto ll zo ult ll grzz gro x(t) tur z (t), gt vr put ll ct rtt. Z Z Z3 X C A A P Y H L L trfort ll uct puo prr, pr l prcpo ovrppozo gl fftt, co l: Y z Z ( () ov ( l F. T. gro-uct l t cotrollo fc l z ( oo l F. T. put cu gcoo vr tur Z ll uct. L rror puo qu r pro co l: [ ] E ( () z Z ll () o fto l F. T. gro-rror:
x E( [ ( )] (3) Tl F. T. goc u ruolo fotl ll l ll proprt rg prt t rvto. Pr tl l fro rfrto llo ch plfcto (ch locch tr pr gl rvt) l qul prt l olo gl gro x(t): X C P Y H Pr quto rgur l coportto rg t rgolzo utlzzro vc lo ch plfcto (ch locch tr pr l rgolzo) l qul prt u olo gl turt z(t) gt rttt ull uct, l gl rfrto x(t)cot. prtcolr ullo. X C u P Z y r H
Prtcolrzzo pr tl tuzo l () h: E z Z( (4) ll qul puo fr l F. T. turo-rror: z Ez z Z( z (5) Co rfrto ll ( ll for polol tr: h: (6) ) x (7) Co pu volt glto, ot ch (, x ( z ( ho lo to otor, ch l poloo crttrtco cclo chuo. L quzo ffrzl ch lg l rror x (t) ll gro x(t) ( tr pr l l ll rror rg t rvto) puo ottr fclt pr ttrforzo ll (7) crtt ll for: E x ) (8) Equzo ffrzl ll rror pr gl rvt: x ( t) t x( t) x( t) ) (9) t t Co procur prfttt log, prto ll (5), potr rcvr ch l quzo ffrzl ch lg l rror z (t) l turo z(t), ( tr pr l l ll rror rg t rgolzo). Nll trttzo ttul o o vluppro ttglo l l ll rror rg co rfrto ll quzo ffrzl cu opr ltoc, pr otr cop, trovr rultt pu gfctv trt rcoro l tor l vlor fl. 3
Clfczo t rvto ll rror rg. U t rvto c tpo ll rpot u gl gro coco δ -() (t) l lt pr t ll rror fto o ullo. Ovvt f rfrto t tl. Dll fzo rv ch: u t tpo h rror fto rpot l gro; u t tpo h rror fto rpot ll rp lr; u t tpo h rror fto rpot ll rp prolc tc. grfc S puo otrr oltr l gut proprt grl: u t tpo rpo rg co u rror ullo pr gr coc or (pot ll potz t ) fror co rror fto pr gr coc or upror. L utlt ll clfczo tp t l ftto ch ll coocz l tpo rvto puo r pror ( prcr l trtoro) l t rpor rg r ofct vr gr coc. Cozo ull ( ffch u t tpo. Co rfrto ll ( ll for (6) puo fclt otrr ch: U t rvto tpo h:... ; ; () Applcho l tor l vlor fl ll: E x ( x (X(; o: puo crvr: x ( ) lx ( t) l t ) ; o vl l () ott: 4
x ( ) l [ ( ) ) ( ) ] () c.v.. L () pr l rror rg ch vrfc u t tpo co gro coco δ -() (t) fuzo coffct polo urtor otor (. E opportuo orvr quto puto ch l () c ch, ffch u t rvto po r tpo, cro ch l F. T. cclo chuo u urtor gro lo pr (-) (co l ( v vr lo (-) zr), prch cop l coffct -. L () ltr prt prtt prr l cozo prch u t rvto tpo rfrt ll truttur ll x (: U t tpo l x ( h uo zro oltplct ll org. ESEMPIO Suppoo volr rlzzr u t rvto tpo co ch, ptt ll truttur tr, l F. T. cclo chuo l for: ; Il t v qu vr rror ullo rpot l gro rror cott rpot ll rp. Dovr uqu r, pr l (): ; co I grl ffch u t rvto tpo l gugo cclo chuo v r ugul ll cott rt. Suppoo volr rlzzr vc u t rvto tpo ; cor ll () ovro r vrfct l rlzo: ; oltr ll clt l gugo co opr, quto co ovr fr oo ch ll ( cop urtor u o l tpo pr potr qu porr co : 5
Auo rlzzr l t fc co rtrozo utr H. Sr qu: G( N( N( ; G( ; G( D( D( N( Qut ult rlzo coo ch ( G( ho lo to poloo urtor. Pr ggugr l tr urtor ll F. T. cclo chuo vo trourlo l urtor ll F. T. cclo prto. Co rfrto llo ch locch v ch pr l t llo tuo co puo ottr ggugo tr l coprtor G( u locco co F. T. pr :. x G y Co quvl fr gr u G( u gl cozo u tr, uo proporzol l gl rror uo proporzol ll u rvt. Alzzro pu vt gl fftt tl ofc ull c l t cclo chuo. CONCLUSIONE: Dll l coffct ( pol coocr l coportto l t rg prt r rzzt ll clt progttul fr ffch o coport coo l opportu pcfch ( prtcolr potro cglr coffct oo ch l t tpo, o ). 6